Let M be a. complete connected Riemannian manifold of dimension n and let £:M → Rn+k
be an isometric immersion into the Euclidean space Rn+k. Let ∇ be the connection on Mn
and let be the Euclidean connection on Rn+k. Also let
denote the second fundamental form B(X, Y) = (
Y)→. Here TP(M) denotes the tangent space at p, NP(M) the normal space and (…)→ the normal component.